Working Both Sides

Abstract

Accepting the importance of Jim Greeno’s work, not just in this volume but throughout his career, I offer this commentary from the position of a researcher who first worked “from the inside out” and who now works “from the outside in.” My identity is that of a mathematics educator with a theoretical commitment to design research. To clarify, for almost seven years I collaborated with Paul Cobb, Koeno Gravemeijer and others in the execution of classroom design experiments in which I acted as the teacher. In these settings, I was working from the inside out to first, in action, make sense of students’ understandings so that I could planfully orchestrate classroom discussions. Later, I would conduct retrospective analyses of my interactions by analyzing from the “outside” what I had previously participated in on the “inside.” In these instances, I worked to understand both the students’ and my learning through normative patterns of engagement. The theoretical lens that I adopted for most of my analyses of the classroom is that of a social constructivist with a strong emphasis on tools. I find Greeno’s levels of accounts of cognition in interaction strengthen my previous orientation by more clearly articulating levels of a progression of conceptual understanding. However, I am left wondering what the means of support are for shifts between the levels. Clearly, having a way to analyze the students’ current abilities or ways of reasoning is crucial. However, I view it as necessary but insufficient for supporting learning. It is this stance that I take in my commentary.